Online retail giant Amazon won an important victory today in its battle for the right to set the price of e-books in Europe, which could see prices fall.

Online rival Apple and four publishing giants have given a commitment to the European Union that they will relax price restrictions on Amazon and other retailers.

The agreement means Amazon can now sell e-books more cheaply if it wishes.

The EU has now ended its competition investigation into Apple and the four publishers — Simon & Schuster, HarperCollins, Hachette Livre and Macmillan.

They had faced claims that they were keeping the price of e-books artificially high.

Joaquin Almunia, the EU’s Competition Commissioner, said: “While each separate publisher and each retailer of e-books are free to choose the type of business relationship they prefer, any form of collusion to restrict or eliminate competition is simply unacceptable.

“The commitments proposed by Apple and the four publishers will restore normal competitive conditions in this new and fast-moving market, to the benefit of the buyers and readers of e-books.”

The EU began its inquiry last year, when its investigators raided the offices of some of the publishers.

Amazon still dominates the e-book market but its victory comes after a torrid time when it has faced sustained criticism in the UK over its corporate tax avoidance.

The online giant has — legally — paid barely any corporation tax in the UK by funnelling most of its revenues via Luxembourg.